The motions of particles may cause chaos. Chaos is an important phenomenon in nonlinearly dynamic systems. In a classical chaos, a particle’s trajectory deviates exponentially from it's initial location due to a small change of initial conditions. In quantum systems, an important probe of chaotic behaviors is out-of-time ordered correlators (OTOCs) [1]}, [2]}, [3]}, [4]}, [5]}. It was first computed by Shenker and Stanford using the eikonal approximation. They found that the Lyapunov exponent is related to the temperature of the black hole [2]}.
